Unbounded non-zero inner product encryption

Abstract

In a non-zero inner product encryption (NIPE) scheme, ciphertexts and keys are associated with vectors from an inner-product space. Decryption of a ciphertext for x→ is allowed by a key for y→ if and only if the inner product 〈x→,y→〉≠0. Existing constructions of NIPE assume the length of the vectors are fixed apriori. We present the first constructions of unbounded non-zero inner product encryption (UNIPE) with constant sized keys. Unbounded here refers to the size of vectors not being pre-fixed during setup. Both constructions, based on bilinear maps, are proven selectively secure under the decisional bilinear Diffie-Hellman (DBDH) assumption.Our constructions are obtained by transforming the unbounded inner product functional encryption (IPFE) schemes of Dufour-Sans and Pointcheval (ACNS 2019), one in the strict domain setting and the other in the permissive domain setting. Interestingly, in the latter case, we prove security from DBDH, a static assumption while the original IPFE scheme relied on an interactive parameterised assumption. In terms of efficiency, features of the IPFE constructions are retained after transformation to NIPE. Notably, the public key and decryption keys have constant size.